)exp. which is here evaluated for three different probability distributions, P(z ): P(z ) = 1 ( σ 2π exp (z ) 2 ) N ov = N exp 2λ

Transcription

1 Electronic Supplementary Material A simple technique for estimating an allowance for uncertain sea-level rise Climatic Change John Hunter, Antarctic Climate & Ecosystems Cooperative Research Centre, Hobart, Tasmania, Australia john.hunter@utas.edu.au A Derivation of Allowances Eq. 7 of main paper is: ( ) µ z + z +z N ov = P(z )exp dz (( ( ( ))/ ) z = N exp z +ln P(z )exp )dz (i) which is here evaluated for three different probability distributions, P(z ): Normal Distribution: If P(z ) is a normal distribution of zero mean and standard deviation, σ, then P(z ) = 1 ( σ 2π exp (z ) 2 ) 2σ 2 (ii) and Eq. (i) becomes N ov = N exp (( )/ z + σ2 2 ) (iii) in which z in the original Gumbel distribution (N in Eq. 6 in main paper) has been replaced by z z σ 2 /(2); the distribution has been shifted vertically by z +σ 2 /(2). Boxcar Distribution: If, P(z ) is a boxcar (uniform) distribution of zero mean and full-width, W (and therefore standard deviation, σ = W/(2 3)), then 1

2 P(z ) = 1 W for W/2 < z < W/2 otherwise 0 (iv) and Eq. (i) becomes (( ( ( ) ))/ 2 W N ov = N exp z +ln ) W sinh 2 (( ( ( )))/ ) σ 3 = N exp z +ln σ 3 sinh (v) in which z in the original Gumbel distribution (N in Eq. 6 in main paper) has been replaced by z z ln( ); the distribution has been shifted vertically by z +ln( ). Raised Cosine Distribution: Finally, if P(z ) is a raised cosine distribution of zero mean and full-width, W (and therefore standard deviation, σ = (W/2) 1/3 2/(π 2 ) = W/(2K) where K = 1/ 1/3 2/(π 2 ) ), then P(z ) = 1 W ( ( )) 2πz 1+cos W for W/2 < z < W/2 otherwise 0 (vi) and Eq. (i) becomes (( ( ( ) ( 2 W N ov = N exp z +ln W sinh (2π/W) 2 )))/ ) 2 1+(2π/W) 2 (( ( ( ) ( Kσ = N exp z +ln Kσ sinh (π/σ) 2 )))/ ) K 2 +(π/σ) 2 (vii) in which z in the original Gumbel distribution (N in Eq. 6 in main paper) has been replaced by z z ln( ); the distribution has been shifted vertically by z +ln( ). Summary: Therefore, the appropriate allowances (Z n, Z b and Z r, for normal, boxcar and raised cosine distributions, respectively) for uncertain sea-level rise, which maintain the same expected number of flooding events in a given period, are 2

3 Z n = z + σ2 2 for a normal distribution, (viii) ( ( ) ) 2 W Z b = z +ln W sinh 2 ( ( )) σ 3 = z +ln σ 3 sinh for a boxcar distribution, and (ix) ( ( ) ( 2 W Z r = z +ln W sinh (2π/W) 2 )) 2 1+(2π/W) 2 ( ( ) ( Kσ = z +ln Kσ sinh (π/σ) 2 )) K 2 +(π/σ) 2 for a raised cosine distribution (x) It may be shown that Z n Z b and Z n Z r for all σ/. A conservative allowance for sea-level rise is therefore Z n (Eq. (viii)). However, the raised cosine distribution (which yields the allowance given by Eq. (x)) is probably the more appropriate, given that there are physical constraints (and hence probable limits) on the rate of future sea-level rise (see Section 5.2 of main paper). B The Uncertainty of the Projections The derivation of the standard error of the best estimate of the projections from the results of the TAR (Third Assessment Report of the Intergovernmental Panel on Climate Change or IPCC) and AR4 (Fourth Assessment Report of the IPCC) is not straightforward. If the projections from individual models were independent, then it would only be necessary to estimate the number of degrees of freedom, n, and to calculate the standard error, σ, from the standard deviation, s, from σ 2 = s2 n (xi) The AR4 projections were based on 19 AOGCMs (Atmosphere-Ocean General Circulation Models), which were run on emission scenarios B1, A1B and A2. The remaining scenarios were modelled using the MAGICC (Model for the Assessment of Greenhouse-gas Induced 3

4 Climate Change) simple climate model (e.g. Meinshausen et al 2011), using empirical time-dependent ratios between pairs of scenarios (one of which was modelled using AOGCMs). It is tempting to assume that the models are independent and to associate the number of degrees of freedom, n, with the number of models used in the preparation of the AR4 projections (of order 20). However, Masson and Knutti (2011) performed a hierarchical clustering of the CMIP3 (phase 3 of the Coupled Model Intercomparison Project; the models reported in AR4) climate models and concluded that, due to widespread sharing of history, algorithms and components between models, the number of structurally different models is small, indicating that the actual number of degrees of freedom is significantly smaller than 20. Pennell and Reichler (2011) statistically analysed the results of 24 CMIP3 models and concluded that the effective number of models was only about 8. Furthermore, due to the strong interdependence of the models, it is likely that important aspects of the physics is either missing or wrong in all models, giving a bias which cannot be deduced from the scatter of model results, and which represents an additional uncertainty. Clear examples of this are the treatment of glaciers, ice caps and ice sheets (for which there is only one series of models contributing to the AR4 results) and the modelling of sulfate aerosols (a number of models sharing common observational data). Due to these considerations, the uncertainty, σ, is here associated with the standard deviation (rather than the standard error) of the projections. C Initial Processing of the GESLA Sea-Level Database The GESLA (Global Extreme Sea-Level Analysis) dataset was initially processed as follows: 1. only files which are at least 30 years in length (defined by the number of months containing at least some data, divided by 12) were selected, 2. non-physical outliers (identified as outliers which did not have any obvious cause, such as a tsunami or a tropical cyclone) and datum shifts (identified by a clear vertical offset, often bracketing a significant data gap) were addressed, either by removal or adjustment of data, 3. known tsunamis were removed, 4. where records were duplicated in separate files, the one which appeared most free of errors was selected, and 5. co-located data covering different time periods was joined, with appropriate adjustment for any datum shift. This resulted in 198 records, of which 166 were unchanged from the original GESLA files, 28 were subject to some modification and 4 were the result of joining records. These records contain both tides and storm surges. 4

5 DARWIN PORT HEDLAND TOWNSVILLE AUSTRALIA BUNDABERG FREMANTLE SYDNEY ADELAIDE MELBOURNE TASMANIA HOBART Figure (i): Results of Australian analysis, indicated by dot diameter. (a) Factor by which frequency of flooding events will increase with a rise in sea level of 0.5 metres (key is lefthand column of dots in the bottom left-hand corner). (b) Sea-level rise allowance (metres) for which conserves frequency of flooding events for the IPCC A1FI Projection based on A1FI emission scenario and AR4-adjusted TAR projections (normal distribution with z = m and σ = m); key is central column of dots in the bottom lefthand corner. (c) Sea-level rise allowance (metres) for 21st century which conserves frequency of flooding events for the 1.0/1.0 m Projection, based on post-ar4 results (raised cosine distribution with z = 1.0 m and W/2 = 1.0 m); key is right-hand column of dots in the bottom left-hand corner. 5

6 Table (i): Range of global sea-level rise from post-ar4 research (after Nicholls et al 2011). a Higher rates are possible for shorter periods. b For the twenty-first century. c For the best palaeo-temperature record. Sea-level Rise Methodological approach Source (m century 1 ) semi-empirical projection b Rahmstorf a palaeo-climate analogue Rohling et al synthesis b Vellinga et al physical-constraint analysis b Pfeffer et al a palaeo-climate analogue Kopp et al semi-empirical projection b Vermeer and Rahmstorf c semi-empirical projection b Grinsted et al 2010 Table (ii): Summary of analyses for specific locations. a Large values such as this indicate that any locations which have been flooded in the past will be flooded on a daily basis with 0.5 m of sea-level rise (the ranges of sea-level variation at Cristóbal and Rikitea are only m). Location Increase in Sea-level rise Sea-level rise frequency of flooding allowance, allowance, twentyevents for sea-level 2100, IPCC A1FI first century, 1.0/ rise of 0.5 m Projection (m) 1.0 m Projection (m) Antofagasta (Chile) 9, Canary Islands (Spain) Cape Town (South Africa) 12, Cristóbal (Panama) 465,000 a Fremantle (Australia) Furuögrund (Sweden) Honningsvåg (Norway) Honolulu (USA) 6, Key West (USA) 5, Kwajalein (Marshall Islands) 15, La Coruña (Spain) Nagasaki (Japan) 1, New York (USA) Oslo (Norway) Rikitea (French Polynesia) 147,000 a Rio de Janeiro (Brazil) San Diego (USA) 3, Seattle (USA) Sheerness (UK) Sydney (Australia) 2, Trieste (Italy) Wellington (New Zealand) 2,

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